Radiometric calibration from noise distributions

ABSTRACT

Technologies that enable correcting for the non-linear relationship between scene irradiance and digital pixel intensity values of an image of the scene produced by a camera. Imaging noise is used as a signal from which a corrective function is derived. Noise distributions from the image are evaluated to determine the radiometric response function of the camera, from which an inverse response function is computed and used for calibration.

BACKGROUND

Many computer vision algorithms rely on the assumption that imageintensities are linearly related to the image irradiance recorded at thecamera sensor. Since most cameras non-linearly alter irradiance valuesfor purposes such as dynamic range compression, this assumptiongenerally does not hold. It is therefore important to calibrate theresponse function of the camera so that the non-linear mapping can beinverted and subsequent algorithms can assume linearity of intensityobservations.

Radiometric calibration aims to estimate the response function ƒ of acamera. The radiometric response function ƒ maps irradiance I that iscaptured at the sensor to the image intensity M that is read from thecamera:

M=ƒ(I)

For vision algorithms and the like that require irradiance values Irather than measured intensity M as input, the inverse response functiong=ƒ⁻¹ needs to be determined so that measured intensities can be madelinear with respect to irradiances. Since response functions faretypically monotonic, they tend to be invertible.

Many conventional methods for estimating a camera response functionrequire as input an image sequence taken with varying exposures from afixed camera. A few methods allow some camera movement or scene motion,but still require changes in exposure level. But in many applicationssuch as those of web cameras, multiple images at different exposurescannot be obtained for radiometric calibration. Accordingly, someprevious methods have been proposed without the need to make adjustmentsin camera exposure settings. But such methods may require assumptionsabout the radiometric response function of a camera that are ofteninvalid. Other previous methods may rely on statistical distributions ofirradiance but may be susceptible to image noise. Previous methods ofradiometric calibration tend to be degraded by imaging noise,particularly by high noise levels.

SUMMARY

The following presents a simplified summary of the disclosure in orderto provide a basic understanding to the reader. This summary is not anextensive overview of the disclosure and it does not identifykey/critical elements of the invention or delineate the scope of theinvention. Its sole purpose is to present some concepts disclosed hereinin a simplified form as a prelude to the more detailed description thatis presented later.

The present examples provide technologies that enable correcting for thenon-linear relationship between scene irradiance and digital pixelintensity values of an image of the scene produced by a camera. Imagingnoise is used as a signal from which a corrective function is derived.Noise distributions from the image are evaluated to determine theradiometric response function of the camera, from which an inverseresponse function is computed and used for calibration.

Many of the attendant features will be more readily appreciated as thesame become better understood by reference to the following detaileddescription considered in connection with the accompanying drawings.

DESCRIPTION OF THE DRAWINGS

The present description will be better understood from the followingdetailed description considered in connection with the accompanyingdrawings, wherein:

FIG. 1 is diagram showing symmetric profiles of noise distributions inthe image radiance domain and the corresponding asymmetric profiles ofthe noise distributions in the observation domain skewed by thenon-linearity of the radiometric response function.

FIG. 2 is a diagram showing an example method for radiometriccalibration of a camera.

FIG. 3 is a diagram showing an example of measuring the degree ofsymmetry of a noise distribution.

FIG. 4 is a block diagram of an example system for radiometricallycalibrating a camera.

FIG. 5 is a diagram showing a chart including an example measured noiseprofile and a corresponding noise profile after calibration.

FIGS. 6A and 6B show examples of incomplete noise distributions.

FIG. 7 is a block diagram showing an example computing environment inwhich the technologies described herein may be implemented.

Like reference numerals are used to designate like parts in theaccompanying drawings.

DETAILED DESCRIPTION

The detailed description provided below in connection with theaccompanying drawings is intended as a description of the presentexamples and is not intended to represent the only forms in which thepresent examples may be constructed or utilized. The description setsforth at least some of the functions of the examples and/or the sequenceof steps for constructing and operating examples. However, the same orequivalent functions and sequences may be accomplished by differentexamples.

Although the present examples are described and illustrated herein asbeing implemented in a computing environment, the system described isprovided as an example and not a limitation. As those skilled in the artwill appreciate, the present examples are suitable for application in avariety of different types of computing environments or the like.

Radiometric calibration is a process of determining the relationshipbetween the physical brightness of a scene (scene radiance) and digitalpixel values of an image of the scene (intensity observations) asproduced by a camera or the like. Typically there is a non-linearrelationship between the scene radiance and image intensity, thenon-linearity varying with different cameras. The technologies describedherein enable correcting for this non-linear relationship by usingimaging noise as a signal from which a corrective function can bederived.

FIG. 1 is diagram showing symmetric profiles 121 and 122 of noisedistributions in the image radiance domain (e.g., on axis 120) and thecorresponding asymmetric profiles 131 and 132 of the noise distributionsin the observation domain (e.g., on axis 130) skewed by thenon-linearity of the radiometric response function 110. The profiles onirradiance axis 120 represent the intensity of light reflected from ascene that enters a camera. The corresponding profiles on observationaxis 130 represent intensity values of an image of the scene captured bya camera. Curve 110 represents the radiometric response function of thecamera that maps the intensity of the irradiance that enters the camerato the observed intensity of the image that is output from the camera.

Irradiance curves 121 and 122 each represent a distribution of noisearound a given irradiance intensity value. Each noise distribution isshown symmetrically distributed around the true intensity value.However, the corresponding observed noise distributions 131 and 132 areasymmetrically skewed. Because of the symmetrically random nature ofnoise sources in the imaging process, asymmetry of the observed noisedistributions is the result of a non-linear transformation that occursin the camera due to the radiometric response function. The terms“radiometric response function” and “response function” are generallyused herein synonymously. The term “inverse response function” generallyrefers to a function that is the inverse of a radiometric responsefunction.

As known to those of skill in the art, noise distributions, such asdistributions 121 and 122, may be derived in a variety of conventionalways. In one example, this may be done by measuring the intensity of apixel over a number of video frames with a fixed camera viewing a staticscene, in another example, this may be done by grouping pixels within animage that are expected to have the same scene intensity. Other methodsor techniques may alternatively or additionally be used to derivesuitable noise distributions.

Noise has widely been considered a nuisance in computer vision, but thetechnologies provided herein make use of noise as a signal forestimating radiometric response functions, even high levels of noise.The technologies provided make use of the symmetry of noisedistributions, which is not affected by noise level. In general, imagingnoise tends to be symmetrical in nature. Since noise in inevitable inimaging, these technologies have wide applicability.

One significant source of imaging noise is the camera itself. Noise isintroduced into intensity observations at multiple points along theimaging pipeline of a camera. The terms “noise” and “imaging noise” andthe like as used herein generally refer to disturbances that cause anobserved intensity value to vary from the actual irradiance intensity ofa scene. Prominent sources of noise may include random noise associatedwith analog to digital (“A/D”) conversion and uneven photon flow fromthe original scene, fixed pattern noise due to differences insensitivity among photon detectors in the imaging array, and darkcurrent noise that results from measurement of thermal radiation withinthe camera. Alternatively or additionally, other sources of imagingnoise may affect observed image intensity. Such noise is generallyconsidered symmetrical in nature.

The terms “irradiance intensity”, “true scene intensity”, “trueintensity value”, and the like as used herein generally refer to theactual scene radiance arriving at a camera. These values are typicallyperturbed by imaging noise before being represented in a digital imageproduced by the camera. The term “observed intensity value” or the likegenerally refers to an intensity value based on scene radiance andpotentially impacted imaging noise. The terms “noise curve”, “curve”,“profile”, “noise distribution”, and the like as used herein typicallyrefer to a representation of the noise characteristics of a cameraproviding the observed intensity values. Such noise characteristics aregenerally represented by a radiometric response function.

FIG. 2 is a diagram showing an example method 200 for radiometriccalibration of a camera. In general, method 200 includes examining noiseprofiles at multiple intensity levels to estimate a radiometric responsefunction describing the noise characteristics of the camera. Theradiometric response function describes the transformation ofsymmetrical noise distributions viewed by the camera into thecorresponding asymmetrical noise distributions output by the camera.Because a radiometric response function is monotonic, an inverseresponse function can be estimated and used to radiometrically calibratethe camera.

Block 210 generally illustrates the imaging process performed by thecamera. Scene irradiance is viewed by the camera resulting in symmetricirradiance noise profiles 212 at each viewed intensity level due to thenoise characteristics of the camera. Camera noise characteristics may bemodeled by a radiometric response function ƒ 214 which describes thetransformation of the viewed symmetrical noise profiles into measuredasymmetric noise profiles 220 at image intensity levels output by thecamera.

Block 230 generally illustrates radiometric calibration of the cameraincluding estimating an inverse response function g 212 based onfunction ƒ 214 that can be applied to image intensity values resultingin projected irradiance noise distributions 234 consistent with thesymmetric irradiance noise profiles 212 originally viewed by the camera.

FIG. 3 is a diagram showing an example of measuring the degree ofsymmetry of a noise distribution 310. Such a noise distribution isgenerally based on multiple samples of a particular intensity. In oneexample, such a noise distribution may be obtained by combining theintensity values from the same pixel of multiple samples of the samescene. The number of such samples may be about 100. In other examples,any suitable technique can be used to obtain a noise distribution,including conventional techniques.

Axis 340 typically indicates intensity level. Peak 311 represents themost frequent intensity level in distribution 310, the distributionmode. The symmetry metric S may be calculated by computing the distancefrom distribution mode 311 to the profile of the distribution atmultiple different heights, e.g., example heights 312 a-312 e. At eachi-th height in the distribution q 310, the distance to the profile onthe left d_(q,i) ⁻ 320 and on the right d_(q,i) ⁺ 330 of peak 311 arerespectively computed. The degree of symmetry of distribution q 310 isthen evaluated as:

$\begin{matrix}{{S(q)} = {{- \frac{1}{n}}{\sum\limits_{i = 1}^{n}\left( \frac{d_{q,i}^{-} - d_{q,i}^{+}}{d_{q,i}^{-} + d_{q,i}^{+}} \right)^{2}}}} & {{Equation}\mspace{14mu} (1)}\end{matrix}$

where n is the number of heights to be evaluated. A larger value of ntypically yields a more accurate result at a cost of greater computationtime, which is generally proportional to n. In one example, a value of20 for n is sufficient. The denominator of Equation (1) normalizes eachterm by the distribution width at the given height. Larger values of S(as S tends to zero) generally indicate greater symmetry. While anysymmetry metric or skewness metric may in principle be used in place ofEquation (1), other metrics may be less sensitive to slight changes indistribution structure.

With the symmetry measure of Equation (1), the inverse response functiong can be computed from a set of collected noise profiles Ω by maximizingthe following energy function so as to maximize the symmetry of all thedistributions in Ω:

$\begin{matrix}{{E\left( {g;\Omega} \right)} = {{\frac{1}{\Omega }{\sum\limits_{q \in \Omega}{S\left( {g;q} \right)}}} = {\frac{1}{\Omega }{\sum\limits_{q \in \Omega}{S\left( {g(q)} \right)}}}}} & {{Equation}\mspace{14mu} (2)}\end{matrix}$

where |Ω| represents the number of noise distributions in set Ω. Thisfunction evaluates the degree of symmetry of noise profiles that areprojected to the irradiance domain by the inverse response function g.

While argmax_(g) E(g) gives the optimal estimate of the inverse responsefunction g, it may be computationally difficult to solve for anon-parametric inverse response function because of the large number ofintensity levels (e.g., 256 intensity levels for 8-bit images).

To facilitate optimization, a parametric model based on a principalcomponents analysis (“PCA”) on a database of real-world responsefunctions may be utilized. The response functions in the database ofresponse functions or the like are first inverted so that the principalcomponents of the inverse response functions can be computed. With theseprincipal components, an inverse response function g can be representedas:

g=g ₀ +Hc   Equation (3)

where g₀ is the mean response function of the inverse response functionsin the database of response functions, H is the matrix whose columns arecomposed of the first N eigenvectors, and c is an N-dimensional vectorof PCA coefficients. In one example the value for N is set to 5. Withthis representation of inverse response functions, the problem istransformed into estimating the N coefficients of c:

$\begin{matrix}{\hat{c} = {\underset{c}{\arg \; \max}{E\left( {g;{g = {g_{0} + {Hc}}}} \right)}}} & {{Equation}\mspace{14mu} (4)}\end{matrix}$

The database of response functions (“DoRF”) typically includes a set ofcaptured response functions from many different cameras that have beeninverted. A model, such as described in Equation (3), may be formedbased on principal components analysis of the major variations of themany inverse response functions in the DoRF. The set of inverse responsefunctions in the DoRF can be indexed by vector c. In the example whereN=5, Equation (3) can be solved for the 5 parameters that describe theinverse response function in the DoRF that best maximizes the energy ofEquation (2), thus maximizing the symmetry of all the distributions inΩ. In alternate example, any number of parameters or dimensions N may beused to model the response functions in the DoRF.

Note that the Intensity axis 340 represents a range of intensity. Asknown to those of skill in the art, pixel values of a digital image aretypically discrete values within such a range. For example, a grayscaleintensity range may be represented using 8 bits to provide 256 possiblegrayscale intensity values ranging from 0 to 255. Similarrepresentations may be used for different color intensity ranges, suchas for the intensity of each of red, green, and blue (“RGB”) or thelike. Alternatively, other scales or bit counts or value ranges may beused to represent various types of scene intensity. The technologiesdescribed herein may be applied to grayscale intensities and/or toindividual or combined color intensities.

FIG. 4 is a block diagram of an example system 400 for radiometricallycalibrating a camera. Example system 400 typically includespre-processing module (“PPM”) 410, inverse response function calculator(“IRFC”) 420, and transformation module (“TRAM”) 430. Interface 402 mayenable system 400 to be accessed and/or controlled by, or to interfacewith, any other system, device, user, camera 490, or the like. Theseelements may be further broken down into sub-elements and/or may becombined in whole or in part with one or more of the other elements orsub-elements. Database of response functions 490 may be distinct fromsystem 400 or may be included as an element of system 400. System 400may be integrated into camera 480 or may be distinct from camera 480.

PPM 410 typically accepts image data from camera 480 or from any othersource of image data, such as a storage device or the like. Such imagedata may be in the form of an image file or the like. The image data mayrepresent a scene or scenes 470 viewed by camera 480 or the like. Theimage data is typically stored and converted to a set of distributions.In particular, one or more asymmetric noise distributions 472 may bederived from the image data, the asymmetry of the noise distributionstypically resulting from imaging noise related to camera 480. PPM 410typically evaluates the image data and calculates a radiometric responsefunction ƒ that describes the asymmetry of distributions 472 relative tothe symmetric noise distributions of the original scene 470, accountingfor the imaging noise. The radiometric response function ƒ may besimilar to or the same as that described in connection with block 210 ofFIG. 2. In general, PPM 410 may be a software module(s), process(es),application(s), firmware routine(s), electronic module(s), device(s), acombination of two or more of the foregoing, or any other pre-processingmeans operable to accept image data input and to derive therefrom a setof asymmetric noise distributions.

IRFC 420 typically calculates the inverse response function g from theradiometric response function ƒ. The inverse response function g may becalculated as described in connection with FIG. 3. IRFC 420 may make useof DoRF 490 (such as that described in connection with FIG. 3) inoptimizing the calculation of g. In general, IRFC 420 may be a softwaremodule(s), process(es), application(s), firmware routine(s), electronicmodule(s), device(s), a combination of two or more of the foregoing, orany other calculation means operable to accept noise distribution(s)and/or response function(s) as input and to derive therefrom an inverseresponse function.

TRAM 430 typically applies inverse response function g to the imagingdata to correct for any imaging noise introduced by camera 480 or thelike, resulting in corrected image data as suggested by symmetricdistribution 440. In this manner, noise, regardless of level, is used asa signal for curing image data of negative effects caused by the noise.In general, TRAM 430 may be a software module(s), process(es),application(s), firmware routine(s), electronic module(s), device(s), acombination of two or more of the foregoing, or any other transformationmeans operable to transform image data based on an inverse responsefunction.

FIG. 5 is a diagram showing a chart 500 including an example measurednoise profile 510 and a corresponding noise profile 520 aftercalibration. Noise profile 510 was measured using a Canon EOS 20D camera(ISO 1600). Chart 500 shows a real-world example of how a measuredasymmetric noise profile is projected using a radiometric responsefunction into a symmetric distribution in the irradiance domain.

FIGS. 6A and 6B show examples of incomplete noise distributions. FIG. 6Ashows a partial distribution of which the upper portion can be used forevaluating the degree of symmetry. FIG. 6B shows a partial distributionthat is typically discarded due to insufficient symmetry data. Noisedistributions may run up against an upper bound (such as shown in FIGS.A and B) or a lower bound or both. Such bounds may be the limits ofirradiance intensity that a camera or the like can measure.

In such cases where noise profiles g(∀ q ε Ω) do not cover the entirerange of irradiance values, there may exist multiple solutions thatresult in symmetry of noise distributions. To avoid this ambiguity,additional constraints on the inverse response function, such assmoothness and monotonicity, may be used. In one example, data from aDoRF (such as that described in connection with FIG. 4) may be used toregulate the solution.

Using the eigenvectors of Equation (3), the PCA coefficients of eachinverse response function in the DoRF may be computed. Then a model oninverse response functions may be constructed by fitting a multivariateGaussian mixture model to the set of PCA coefficients:

$\begin{matrix}{{p(g)} = {\sum\limits_{i = 1}^{K}{\alpha_{i}{\left( {{g;u_{i}},\sum\limits_{i}} \right)}}}} & {{Equation}\mspace{14mu} (5)}\end{matrix}$

where N represents a normal distribution with mean μ_(i) and covariancematrix Σ_(i). In one example, the value of K is empirically set to 5,and the mixture model is obtained using a conventional cross-entropymethod. Further, the likelihood of the degree of symmetry may be modeledas:

$\begin{matrix}{{p\left( {\Omega g} \right)} = {\frac{1}{Z}{\exp \left( {{- \lambda}\; {E\left( {g;\Omega} \right)}} \right)}}} & {{Equation}\mspace{14mu} (6)}\end{matrix}$

which is a variation of Equation (2), where Z is the normalizationfactor, and where it is a regularization coefficient which, in oneexample, is empirically set to 10⁴.

The optimal coefficients ĉ that define the inverse response function gmay be solved for in the following maximum a posteriori (MAP) problem:

$\begin{matrix}{\hat{c} = {{\underset{c}{\arg \; \max}\; {p\left( {{g(c)}\Omega} \right)}} = {\underset{c}{\arg \; \max}\; {p\left( {\Omega {g(c)}} \right)}{p\left( {g(c)} \right)}}}} & {{Equation}\mspace{14mu} (7)}\end{matrix}$

Inserting Equations (5) and (6) into the logarithmic form of Equation(7) results in:

$\begin{matrix}{\hat{c} = {{\underset{c}{\arg \; \min}\; \lambda \; {E\left( {{g(c)};\Omega} \right)}} - {\log \; {p\left( {g(c)} \right)}}}} & {{Equation}\mspace{14mu} (8)}\end{matrix}$

where the optimized coefficients ĉ yield an estimate of the inverseresponse function as g=g₀+Hc.

FIG. 7 is a block diagram showing an example computing environment 700in which the technologies described herein may be implemented. Asuitable computing environment may be implemented with numerous generalpurpose or special purpose systems. Examples of well known systems mayinclude, but are not limited to, cell phones, digital cameras, personaldigital assistants (“PDA”), personal computers (“PC”), hand-held orlaptop devices, microprocessor-based systems, multiprocessor systems,servers, workstations, consumer electronic devices, set-top boxes, andthe like.

Computing environment 700 typically includes a general-purpose computingsystem in the form of a computing device 701 coupled to variouscomponents, such as peripheral devices 702, 703, 704 and the like.System 700 may couple to various other components, such as input devices703, including voice recognition, touch pads, buttons, keyboards and/orpointing devices, such as a mouse or trackball, via one or moreinput/output (“I/O”) interfaces 712. The components of computing device701 may include one or more processors (including central processingunits (“CPU”), graphics processing units (“GPU”), microprocessors(“μP”), and the like) 707, system memory 709, and a system bus 708 thattypically couples the various components. Processor 707 typicallyprocesses or executes various computer-executable instructions tocontrol the operation of computing device 701 and to communicate withother electronic and/or computing devices, systems or environment (notshown) via various communications connections such as a networkconnection 714 or the like. System bus 708 represents any number ofseveral types of bus structures, including a memory bus or memorycontroller, a peripheral bus, a serial bus, an accelerated graphicsport, a processor or local bus using any of a variety of busarchitectures, and the like.

System memory 709 may include computer readable media in the form ofvolatile memory, such as random access memory (“RAM”), and/ornon-volatile memory, such as read only memory (“ROM”) or flash memory(“FLASH”). A basic input/output system (“BIOS”) may be stored innon-volatile or the like. System memory 709 typically stores data,computer-executable instructions and/or program modules comprisingcomputer-executable instructions that are immediately accessible toand/or presently operated on by one or more of the processors 707.

Mass storage devices 704 and 710 may be coupled to computing device 701or incorporated into computing device 701 via coupling to the systembus. Such mass storage devices 704 and 710 may include non-volatile RAM,a magnetic disk drive which reads from and/or writes to a removable,non-volatile magnetic disk (e.g., a “floppy disk”) 705, and/or anoptical disk drive that reads from and/or writes to a non-volatileoptical disk such as a CD ROM, DVD ROM 706. Alternatively, a massstorage device, such as hard disk 710, may include non-removable storagemedium. Other mass storage devices may include memory cards, memorysticks, tape storage devices, and the like.

Any number of computer programs, files, data structures, and the likemay be stored in mass storage 710, other storage devices 704, 705, 706and system memory 709 (typically limited by available space) including,by way of example and not limitation, operating systems, applicationprograms, data files, directory structures, computer-executableinstructions, and the like.

Output components or devices, such as display device 702, may be coupledto computing device 701, typically via an interface such as a displayadapter 711. Output device 702 may be a liquid crystal display (“LCD”).Other example output devices may include printers, audio outputs, voiceoutputs, cathode ray tube (“CRT”) displays, tactile devices or othersensory output mechanisms, or the like. Output devices may enablecomputing device 701 to interact with human operators or other machines,systems, computing environments, or the like. A user may interface withcomputing environment 700 via any number of different I/O devices 703such as a touch pad, buttons, keyboard, mouse, joystick, game pad, dataport, and the like. These and other I/O devices may be coupled toprocessor 707 via I/O interfaces 712 which may be coupled to system bus708, and/or may be coupled by other interfaces and bus structures, suchas a parallel port, game port, universal serial bus (“USB”), fire wire,infrared (“IR”) port, and the like.

Computing device 701 may operate in a networked environment viacommunications connections to one or more remote computing devicesthrough one or more cellular networks, wireless networks, local areanetworks (“LAN”), wide area networks (“WAN”), storage area networks(“SAN”), the Internet, radio links, optical links and the like.Computing device 701 may be coupled to a network via network adapter 713or the like, or, alternatively, via a modem, digital subscriber line(“DSL”) link, integrated services digital network (“ISDN”) link,Internet link, wireless link, or the like.

Communications connection 714, such as a network connection, typicallyprovides a coupling to communications media, such as a network.Communications media typically provide computer-readable andcomputer-executable instructions, data structures, files, programmodules and other data using a modulated data signal, such as a carrierwave or other transport mechanism. The term “modulated data signal”typically means a signal that has one or more of its characteristics setor changed in such a manner as to encode information in the signal. Byway of example, and not limitation, communications media may includewired media, such as a wired network or direct-wired connection or thelike, and wireless media, such as acoustic, radio frequency, infrared,or other wireless communications mechanisms.

Power source 790, such as a battery or a power supply, typicallyprovides power for portions or all of computing environment 700. In thecase of the computing environment 700 being a mobile device or portabledevice or the like, power source 790 may be a battery. Alternatively, inthe case computing environment 700 is a desktop computer or server orthe like, power source 790 may be a power supply designed to connect toan alternating current (“AC”) source, such as via a wall outlet.

Some mobile devices may not include many of the components described inconnection with FIG. 7. For example, an electronic badge may becomprised of a coil of wire along with a simple processing unit 707 orthe like, the coil configured to act as power source 790 when inproximity to a card reader device or the like. Such a coil may also beconfigure to act as an antenna coupled to the processing unit 707 or thelike, the coil antenna capable of providing a form of communicationbetween the electronic badge and the card reader device. Suchcommunication may not involve networking, but may alternatively begeneral or special purpose communications via telemetry, point-to-point,RF, IR, audio, or other means. An electronic card may not includedisplay 702, I/O device 703, or many of the other components describedin connection with FIG. 7. Other mobile devices that may not includemany of the components described in connection with FIG. 7, by way ofexample and not limitation, include electronic bracelets, electronictags, implantable devices, and the like.

Those skilled in the art will realize that storage devices utilized toprovide computer-readable and computer-executable instructions and datacan be distributed over a network. For example, a remote computer orstorage device may store computer-readable and computer-executableinstructions in the form of software applications and data. A localcomputer may access the remote computer or storage device via thenetwork and download part or all of a software application or data andmay execute any computer-executable instructions. Alternatively, thelocal computer may download pieces of the software or data as needed, ordistributively process the software by executing some of theinstructions at the local computer and some at remote computers and/ordevices.

Those skilled in the art will also realize that, by utilizingconventional techniques, all or portions of the software'scomputer-executable instructions may be carried out by a dedicatedelectronic circuit such as a digital signal processor (“DSP”),programmable logic array (“PLA”), discrete circuits, and the like. Theterm “electronic apparatus” may include computing devices or consumerelectronic devices comprising any software, firmware or the like, orelectronic devices or circuits comprising no software, firmware or thelike.

The term “firmware” typically refers to executable instructions, code,data, applications, programs, or the like maintained in an electronicdevice such as a ROM. The term “software” generally refers to executableinstructions, code, data, applications, programs, or the like maintainedin or on any form of computer-readable media. The term“computer-readable media” typically refers to system memory, storagedevices and their associated media, and the like.

In view of the many possible embodiments to which the principles of thepresent invention and the forgoing examples may be applied, it should berecognized that the examples described herein are meant to beillustrative only and should not be taken as limiting the scope of thepresent invention. Therefore, the invention as described hereincontemplates all such embodiments as may come within the scope of thefollowing claims and any equivalents thereto.

1. A method for performing radiometric calibration comprising:constructing a set of noise distributions based on intensity values of adigital image of a scene; measuring a degree of symmetry of each of theset of noise distributions, wherein the degree of symmetry indicatesimaging noise; computing an inverse response function based on thedegree of symmetry of each of the set of noise distributions; andtransforming the digital image using the inverse response function,wherein the radiometric calibration is based on the imaging noise. 2.The method of claim 1 further comprising computing a radiometricresponse function based on a degree of symmetry of at least one noisedistribution of the set of noise distributions.
 3. The method of claim 1wherein the measuring the degree of symmetry is based on the equation:${S(q)} = {{- \frac{1}{n}}{\sum\limits_{i = 1}^{n}\left( \frac{d_{q,i}^{-} - d_{q,i}^{+}}{d_{q,i}^{-} + d_{q,i}^{+}} \right)^{2}}}$where S represents the degree of symmetry, and where q represents anoise distribution of the set of noise distributions, and where d_(q,i)⁻ represents a left distance from the left of a peak to a profile of thenoise distribution at an i-th height of the noise distribution, andwhere d_(q,i) ⁺ represents a right distance from the right of the peakto the profile at the i-th height, and where n is a number of heightsbeing evaluated.
 4. The method of claim 1 wherein computing the inverseresponse function is based on maximizing the energy function:${E\left( {g;\Omega} \right)} = {{\frac{1}{\Omega }{\sum\limits_{q \in \Omega}{S\left( {g;q} \right)}}} = {\frac{1}{\Omega }{\sum\limits_{q \in \Omega}{S\left( {g(q)} \right)}}}}$where g represents the inverse response function, and where |Ω|represents a number of the noise distributions in Ω, the set of noisedistributions, where S represents the degree of symmetry, and where qrepresents a noise distribution of the set of noise distributions Ω. 5.The method of claim 1 wherein the inverse response function isrepresented as:g=g ₀ +Hc where g₀ is a mean response function of a plurality ofresponse functions, and where H is a matrix whose columns are composedof N eigenvectors, and where c is an N-dimensional vector of principalcomponents analysis coefficients.
 6. The method of claim 1 wherein thecomputing the inverse response function comprises selecting an inverseresponse function from a database of inverse response functions whereinthe selected inverse response function is indexed by a set ofcoefficients of a parametric model of the inverse response functions inthe database.
 7. A system for performing a radiometric calibrationcomprising: a radiometric response function calculator operable toderive a set of noise distributions from a digital image of a scene; aninverse response function calculator operable to calculate a symmetrymetric for each of the noise distributions of the set of noisedistributions, the symmetry metric indicating imaging noise, andoperable to compute an inverse response function based on each of thenoise distributions of the set of noise distributions; and atransformation module is operable to perform a transformation thedigital image based on the inverted response function, wherein thetransformation is based on the imaging noise.
 8. The system of claim 7wherein the radiometric response function calculator is further operableto calculate a radiometric response function based on a symmetry metricof at least one noise distribution of the set of noise distributions. 9.The system of claim 7 wherein the symmetry metric is based on theequation:${S(q)} = {{- \frac{1}{n}}{\sum\limits_{i = 1}^{n}\left( \frac{d_{q,i}^{-} - d_{q,i}^{+}}{d_{q,i}^{-} + d_{q,i}^{+}} \right)^{2}}}$where S represents the degree of symmetry, and where q represents anoise distribution of the set of noise distributions, and where d_(q,i)⁻ represents a left distance from the left of a peak to a profile of thenoise distribution at an i-th height of the noise distribution, a whered_(q,i) ⁺ represents a right distance from the right of the peak to theprofile at the i-th height, and where n is a number of heights beingevaluated.
 10. The system of claim 7 wherein the inverse responsefunction is based on maximizing the energy function:${E\left( {g;\Omega} \right)} = {{\frac{1}{\Omega }{\sum\limits_{q \in \Omega}{S\left( {g;q} \right)}}} = {\frac{1}{\Omega }{\sum\limits_{q \in \Omega}{S\left( {g(q)} \right)}}}}$where g represents the inverse response function, and where |Ω|represents a number of the noise distributions in Ω, the set of noisedistributions, where S represents the symmetry metric, and where qrepresents a noise distribution of the set of noise distributions Ω. 11.The system of claim 7 wherein inverse response function is representedas:g=g ₀ +Hc where g₀ is a mean response function of a plurality ofresponse functions, and where H is a matrix whose columns are composedof N eigenvectors, and where c is an N-dimensional vector of principalcomponents analysis coefficients.
 12. The system of claim 7 wherein theinverse response function is computed by selecting an inverse responsefunction from a database of inverse response functions wherein theinverse response functions are captured from different cameras.
 13. Thesystem of claim 7 wherein, if the noise distributions of the set ofnoise distributions do not cover an entire range of irradiance values,the inverse response function is computed by fitting a multivariatemixture model to a set of coefficients.
 14. The system of claim 7further comprising: a database of response functions captured fromdifferent cameras; and a parametric model based on principal componentanalysis of the response functions of the database.
 15. Acomputer-readable medium comprising computer-readable instructions thatembody a method for performing radiometric calibration comprising:constructing a set of noise distributions based on intensity values of adigital image of a scene; measuring a degree of symmetry of each of theset of noise distributions, wherein the degree of symmetry indicatesimaging noise; computing an inverse response function based on thedegree of symmetry of each of the set of noise distributions; andtransforming the digital image using the inverse response function,wherein the radiometric calibration is based on the imaging noise. 16.The computer-readable medium of claim 15, the method further comprisingcomputing a radiometric response function based on a degree of symmetryof at least one noise distribution of the set of noise distributions.17. The computer-readable medium of claim 15 wherein the measuring thedegree of symmetry is based on the equation:${S(q)} = {{- \frac{1}{n}}{\sum\limits_{i = 1}^{n}\left( \frac{d_{q,i}^{-} - d_{q,i}^{+}}{d_{q,i}^{-} + d_{q,i}^{+}} \right)^{2}}}$where S represents the degree of symmetry, and where q represents anoise distribution of the set of noise distributions, and where d_(q,i)⁻ represents a left distance from the left of a peak to a profile of thenoise distribution at an i-th height of the noise distribution, a whered_(q,i) ⁺ represents a right distance from the right of the peak to theprofile at the i-th height, and where n is a number of heights beingevaluated.
 18. The computer-readable medium of claim 15 whereincomputing the inverse response function is based on maximizing theenergy function:${E\left( {g;\Omega} \right)} = {{\frac{1}{\Omega }{\sum\limits_{q \in \Omega}{S\left( {g;q} \right)}}} = {\frac{1}{\Omega }{\sum\limits_{q \in \Omega}{S\left( {g(q)} \right)}}}}$where g represents the inverse response function, and where |Ω|represents a number of the noise distributions in Ω, the set of noisedistributions, where S represents the degree of symmetry, and where qrepresents a noise distribution of the set of noise distributions Ω. 19.The computer-readable medium of claim 15 wherein the inverse responsefunction is represented as:g=g ₀ ′Hc where g₀ is a mean response function of a plurality ofresponse functions, and where H is a matrix whose columns are composedof N eigenvectors, and where c is an N-dimensional vector of principalcomponents analysis coefficients.
 20. The computer-readable medium ofclaim 15 wherein the computing the inverse response function comprisesselecting an inverse response function from a database of inverseresponse functions wherein the selected inverse response function isindexed by a set of coefficients of a parametric model of the inverseresponse functions in the database.